A collocation method for solving singular integro-differential equations

This paper describes a collocation method for numerically solving Cauchy-type linear singular integro-differential equations. The numerical method is based on the transformation of the integro-differential equation into an integral equation, and then applying a collocation method to solve the latter. The collocation points are chosen as the Chebyshev nodes. Uniform convergence of the resulting method is then discussed. Numerical examples are presented and solved by the numerical techniques.

Convolutions and zeros of orthogonal polynomials

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Nonlinear Dynamics and Control of an Ideal/Nonideal Load Transportation System With Periodic Coefficients

In this paper, a loads transportation system in platforms or suspended by cables is considered. It is a monorail device and is modeled as an inverted pendulum built on a car driven by a dc motor the governing equations of motion were derived via Lagrange's equations. In the mathematical model we consider the interaction between the dc motor and the dynamical system, that is, we have a so called nonideal periodic problem. The problem is analyzed, qualitatively, through the comparison of the stability diagrams, numerically obtained, for several motor torque constants. Furthermore, we also analyze the problem quantitatively using the Floquet multipliers technique. Finally, we devise a control for the studied nonideal problem. The method that was used for analysis and control of this nonideal periodic system is based on the Chebyshev polynomial exponsion, the Picard iterative method, and the Lyapunov-Floquet transformation (L-F transformation). We call it Sinha's theory.

On a control of a non-ideal mono-rail system with periodics coefficients

In this work, the problem in the loads transport (in platforms or suspended by cables) it is considered. The system in subject is composed for mono-rail system and was modeled through the system: inverted pendulum, car and motor and the movement equations were obtained through the Lagrange equations. In the model, was considered the interaction among of the motor and system dynamics for several potencies motor, that is, the case studied is denominated a non-ideal periodic problem. The non-ideal periodic problem dynamics was analyzed, qualitatively, through the comparison of the stability diagrams, numerically obtained, for several motor torque constants. Furthermore, one was made it analyzes quantitative of the problem through the analysis of the Floquet multipliers. Finally, the non-ideal problem was controlled. The method that was used for analysis and control of non-ideal periodic systems is based on the Chebyshev polynomial expansion, in the Picard iterative method and in the Lyapunov-Floquet transformation (L-F trans formation). This method was presented recently in [3-9].

On non-linear dynamics and a periodic control design applied to the potential of membrane action

The Fitzhugh-Nagumo (fn) mathematical model characterizes the action potential of the membrane. The dynamics of the Fitzhugh-Nagumo model have been extensively studied both with a view to their biological implications and as a test bed for numerical methods, which can be applied to more complex models. This paper deals with the dynamics in the (FH) model. Here, the dynamics are analyzed, qualitatively, through the stability diagrams to the action potential of the membrane. Furthermore, we also analyze quantitatively the problem through the evaluation of Floquet multipliers. Finally, the nonlinear periodic problem is controlled, based on the Chebyshev polynomial expansion, the Picard iterative method and on Lyapunov-Floquet transformation (L-F transformation).

Identification of structural parameters for active vibration control

The study of algorithms for active vibration control in flexible structures became an area of enormous interest for some researchers due to the innumerable requirements for better performance in mechanical systems, as for instance, aircrafts and aerospace structures. Intelligent systems, constituted for a base structure with sensors and actuators connected, are capable to guarantee the demanded conditions, through the application of diverse types of controllers. For the project of active controllers it is necessary, in general, to know a mathematical model that enable the representation in the space of states, preferential in modal coordinates to permit the truncation of the system and reduction in the order of the controllers. For practical applications of engineering, some mathematical models based in discrete-time systems cannot represent the physical problem, therefore, techniques of identification of system parameters must be used. The techniques of identification of parameters determine the unknown values through the manipulation of the input (disturbance) and output (response) signals of the system. Recently, some methods have been proposed to solve identification problems although, none of them can be considered as being universally appropriate to all the situations. This paper is addressed to an application of linear quadratic regulator controller in a structure where the damping, stiffness and mass matrices were identified through Chebyshev's polynomial functions.

Análise da estabilidade de sistemas dinâmicos periódicos usando Teoria de Sinha

Pós-graduação em Matemática - IBILCE

Diagnose de falhas em sistemas rotativos com excitações desconhecidas, através da metodologia dos observadores de estado

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Técnica de identificação de parâmetros no domínio do tempo utilizando funções ortogonais

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Diagnóstico de falhas via observadores de estado com excitações desconhecidas, identificadas via funções ortogonais

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Identificação de parâmetros em sistemas rotativos utilizando funções de otimização e observadores de estado

Pós-graduação em Engenharia Mecânica - FEIS

The dynamic behavior of a parametrically excited time-periodic MEMS taking into account parametric errors

Micro-electromechanical systems (MEMS) are micro scale devices that are able to convert electrical energy into mechanical energy or vice versa. In this paper, the mathematical model of an electronic circuit of a resonant MEMS mass sensor, with time-periodic parametric excitation, was analyzed and controlled by Chebyshev polynomial expansion of the Picard interaction and Lyapunov-Floquet transformation, and by Optimal Linear Feedback Control (OLFC). Both controls consider the union of feedback and feedforward controls. The feedback control obtained by Picard interaction and Lyapunov-Floquet transformation is the first strategy and the optimal control theory the second strategy. Numerical simulations show the efficiency of the two control methods, as well as the sensitivity of each control strategy to parametric errors. Without parametric errors, both control strategies were effective in maintaining the system in the desired orbit. On the other hand, in the presence of parametric errors, the OLFC technique was more robust.

La base di Bernstein in spazi polinomiali generalizzati

Nella tesi si illustra il passaggio dagli spazi polinomiali agli spazi polinomiali generalizzati, gli spazi di Chebyshev estesi (spazi EC), e viene dato un metodo per costruirli a partire da opportuni sistemi di funzioni dette funzioni peso. Successivamente si tratta il problema dell'esistenza di un analogo della base di Bernstein negli spazi EC: si presenta, in analogia ad una particolare costruzione nel caso polinomiale, una dimostrazione costruttiva dell'esistenza di tale base. Infine viene studiato il problema delle lunghezze critiche di uno spazio EC: si tratta di determinare l'ampiezza dell'intervallo oltre la quale lo spazio considerato perde le proprietà di uno spazio EC, o non possiede più una base di Bernstein generalizzata; l'approccio adottato è di tipo sperimentale: nella tesi sono presentati i risultati ottenuti attraverso algoritmi di ricerca che analizzano le proprietà delle funzioni di transizione e ne traggono informazioni sullo spazio di studio.

La base di Bernstein in spazi polinomiali generalizzati a tratti

Le funzioni polinomiali possono essere utilizzate per approssimare le funzioni continue. Il vantaggio è che i polinomi, le loro derivate e primitive, possono essere rappresentati in maniera semplice attraverso i loro coefficienti ed esistono algoritmi stabili e veloci per valutarli. Inoltre gli spazi polinomiali godono di numerose proprietà importanti. In questo lavoro ci occuperemo di altri spazi funzionali, noti in letteratura come spazi di Chebyshev o polinomi generalizzati, per ragioni di riproducibilità. Infatti ciò che si ottiene attraverso i polinomi è soltanto una approssimazione che spesso risulta essere insufficiente. E' importante, quindi, considerare degli spazi in cui sia possibile avere una rappresentazione esatta di curve. Lo studio di questi spazi è possibile grazie alla potenza di elaborazione degli attuali calcolatori e al buon condizionamento di opportune basi di rappresentazione di questi spazi. Negli spazi polinomiali è la base di Bernstein a garantire quanto detto. Negli spazi di Chebyshev si definisce una nuova base equivalente. In questo lavoro andremo oltre gli spazi di Chebyshev ed approfondiremo gli spazi di Chebyshev a tratti, ovvero gli spazi formati dall'unione di più spazi del tipo precedente. Si dimostrerà inoltre l'esistenza di una base a tratti con le stesse proprietà della base di Bernstein per gli spazi polinomiali.

An integrated environment for filter design

Analog filters and direct digital filters are implemented using digital signal processing techniques. Specifically, Butterworth, Elliptic, and Chebyshev filters are implemented using the Motorola 56001 Digital Signal Processor by the integration of three software packages: MATLAB, C++, and Motorola's Application Development System. The integrated environment allows the novice user to design a filter automatically by specifying the filter order and critical frequencies, while permitting more experienced designers to take advantage of MATLAB's advanced design capabilities. This project bridges the gap between the theoretical results produced by MATLAB and the practicalities of implementing digital filters using the Motorola 56001 Digital Signal Processor. While these results are specific to the Motorola 56001 they may be extended to other digital signal processors. MATLAB handles the filter calculations, a C++ routine handles the conversion to assembly code, and the Motorola software compiles and transmits the code to the processor